東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

A short book on long sums = infinite...

Gouvea, Fernando Q.

FindBook

Google Book

Amazon

博客來

A short book on long sums = infinite series for calculus students /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A short book on long sums/ by Fernando Q. Gouvêa.
其他題名:	infinite series for calculus students /
作者:	Gouvea, Fernando Q.
出版者:	Cham :Springer Nature Switzerland : : 2023.,
面頁冊數:	xi, 145 p. :ill., digital ;24 cm.
內容註:	- To the reader -- Getting close with lines -- Getting closer with polynomials -- Going all the way: Convergence -- Power series -- Distant mountains -- Appendix A: SageMath: A (very) short introduction -- Appendix B: Why I do it this way -- Bibliography.
Contained By:	Springer Nature eBook
標題:	Power series. -
電子資源:	https://doi.org/10.1007/978-3-031-37557-6
ISBN:	9783031375576

A short book on long sums = infinite series for calculus students /
Gouvea, Fernando Q.

A short book on long sumsinfinite series for calculus students /[electronic resource] :by Fernando Q. Gouvêa. - Cham :Springer Nature Switzerland :2023. - xi, 145 p. :ill., digital ;24 cm. - Readings in mathematics,2945-5847. - Readings in mathematics..

- To the reader -- Getting close with lines -- Getting closer with polynomials -- Going all the way: Convergence -- Power series -- Distant mountains -- Appendix A: SageMath: A (very) short introduction -- Appendix B: Why I do it this way -- Bibliography.

This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series-and infinite series in general-are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor's guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.

ISBN: 9783031375576

Standard No.: 10.1007/978-3-031-37557-6doiSubjects--Topical Terms:

711330
Power series.

LC Class. No.: QA295

Dewey Class. No.: 515.2432

A short book on long sums = infinite series for calculus students /
LDR:02829nmm a2200337 a 4500 001 2390089
003 DE-He213
005 20231207000123.0
006 m d
007 cr nn 008maaau
008 250916s2023 sz s 0 eng d
020 $a 9783031375576 $q (electronic bk.)
020 $a 9783031375569 $q (paper)
024 7 $a 10.1007/978-3-031-37557-6 $2 doi
035 $a 978-3-031-37557-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA295
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515.2432 $2 23
090 $a QA295 $b .G719 2023
100 1 $a Gouvea, Fernando Q. $3 2700987
245 1 2 $a A short book on long sums $h [electronic resource] : $b infinite series for calculus students / $c by Fernando Q. Gouvêa.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2023.
300 $a xi, 145 p. : $b ill., digital ; $c 24 cm.
490 1 $a Readings in mathematics, $x 2945-5847
505 0 $a - To the reader -- Getting close with lines -- Getting closer with polynomials -- Going all the way: Convergence -- Power series -- Distant mountains -- Appendix A: SageMath: A (very) short introduction -- Appendix B: Why I do it this way -- Bibliography.
520 $a This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series-and infinite series in general-are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor's guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.
650 0 $a Power series. $3 711330
650 0 $a Series, Infinite. $3 629846
650 1 4 $a Sequences, Series, Summability. $3 897266
650 2 4 $a Analysis. $3 891106
650 2 4 $a Real Functions. $3 891265
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Readings in mathematics. $3 3609269
856 4 0 $u https://doi.org/10.1007/978-3-031-37557-6
950 $a Mathematics and Statistics (SpringerNature-11649)